We use GCN [1]} with edge weights as an encoder for the node-classification task, and the node-wise expression is as follows.
\(\mathbf {h}_{v}^{(k)}=\Theta ^{\top } \sum _{u \in \mathcal {N}_v \cup \lbrace v\rbrace } \frac{e_{u, v}}{\sqrt{\hat{d}_{u} \hat{d}_{v}}} \mathbf {h}_{u}^{(k-1)}\) 
